ICESat-2 provides precise laser altimetry from the Advanced Topographic Laser Altimeter System (ATLAS). The high-frequency acquisition of ATLAS provides continuous along-track photon returns along three pairs of weak and strong beam tracks. Each pair of beams has an intra-pair separation of 90 m, and an inter-pair separation of 3.3 km . After launch, the mean effective laser footprint diameter of ATLAS was found to be ∼ 11 m . ICESat-2 ATL03 returns have a geolocation uncertainty of ∼ 4.4 ± 6 m . Launched in 2018, ICESat-2 has a 91 d polar orbiting cycle but it points off-nadir outside of the polar regions to increase coverage and to map vegetation, repeating reference ground tracks in mid-latitudes every 3 years only. This infrequency of repeat tracks makes it impractical to monitor snow depth on the watershed scale in mid-latitudes by comparing snow-off and snow-on ICESat-2 crossovers. The spatio-temporal restriction caused by infrequent mid-latitude ICESat-2 crossovers can be circumvented by comparing ICESat-2 measurements to independently collected high-resolution snow-free DTMs . Additionally, ICESat-2's off-pointing angle can be increased up to 10° to target a point of interest, resulting in up to roughly monthly to bi-monthly acquisitions when tasked and increasing the likelihood for clear sky conditions and usable ground observations. We conduct our analysis using observations from four Idaho study sites for which ICESat-2 acquisitions were tasked to overpass an automatic weather station (AWS) within each site. ICESat-2 was tasked so that every track within a 30 km radius of the AWSs were shifted to target the AWS, thus enabling the direct comparison of ICESat-2 and situ snow depth data from 2020–2024, as described in Sect. 3.

The ICESat-2 team releases several standard ICESat-2 products designed for different applications. For this study we use a hybridized ATL06-like data product calculated from the Global Geolocated Photon Data product (ATL03) and based on two higher level ICESat-2 product algorithms: the Land Water Vegetation Elevation product (ATL08) photon classification and the Land Ice Elevation product (ATL06) surface elevation algorithm . ATL08 uses a surface finding algorithm to identify the ground and top of canopy within the photon signal cloud (ATL03); photons are classified as ground, canopy, top of canopy, or noise returns . ATL08 parses the classified photons into 100 m segments with 0 % overlap between each segment. At Reynolds Creek Experimental Watershed (Reynolds Creek), one of our Idaho study sites, ATL08-derived snow depths calculated using a 1 m resolution airborne lidar-derived snow-free reference DTM have an estimated normalized median absolute deviation (NMAD) error estimate of 0.95 m . ATL06 is designed for observing ice sheets and glaciers where differences in surface elevation must be resolved on the order of centimeters in order to capture important variations in snow and ice volume. As these land-ice surfaces are vegetation free, ATL06 does not include vegetation filtering. ATL06 calculates ground elevation from the centerpoint of a linear fit to the ATL03 signal photons within a 40 m segment with 50 % overlap between segments, resulting in an estimate of the mean ground elevation every 20 m . ATL06 accounts for temporary photon detector saturation due to strong reflectance over snowy surfaces, improving snow elevation accuracy. In rough snow-covered terrain, comparable to our mountain study sites, ATL06 is expected to have a better vertical accuracy than the aforementioned ATL08 product. However, ATL06 can have a positive elevation bias in forested terrain due to a lack of vegetation filtering. When compared to a 15 m resolution Airborne Snow Observatory (ASO) DTM for Tuolumne Basin in California, ATL06-derived snow depths have a NMAD of 0.60–1.16 m . In this study we make use of the strengths of both algorithms using a hybridized data product (ATL06_SR) that incorporates ATL08 vegetation filtering and the ATL06 algorithm into an ATL06-like product . ATL06_SR is calculated by applying the ATL06 function to ATL08-identified ATL03 ground photon returns instead of the ATL03-identified ground photon returns. The generation of ATL06_SR is discussed in more detail in Sect. 3.1. As applied in this paper, ATL06_SR includes ATL08's vegetation filtering but does not include the first photon bias correction, which can result in up to ∼ 2 cm of bias, or the transit pulse shape bias, which can result in up to ∼ 1 cm of bias. ATL06_SR derived daily median snow depths have a Root Mean Square Error (RMSE) of 0.18 m in Tuolumne Basin compared to a 3 m resolution ASO DTM and a RMSE of 0.33 m in the Methow Valley in Washington compared to a 1 m resolution airborne lidar DTM . Thus, we use the hybridized ATL06_SR product to calculate snow depth because of its superior precision relative to either stand-alone product .

We evaluate ICESat-2 snow depths over four mountain study sites across southern and central Idaho: Reynolds Creek Experimental Watershed (Reynolds Creek), Banner Summit (Banner Summit), Dry Creek Experimental Watershed (Dry Creek), and Mores Creek Summit (Mores Creek). These four sites span an array of vegetation cover, elevation ranges, terrain complexity, and average snow depth. Each site has a high-resolution snow-free airborne lidar DTM freely available acquired during various campaigns as described in the following site descriptions. For each site, the area of interest (AOI) was defined to match the extent of the site's snow-free DTM. To validate the ICESat-2 snow depths, we use in situ snow depths from automatic weather stations (AWS) within each study site. Each site has a SNOwpack TELemetry Network (SNOTEL) AWS; some sites have additional AWSs described below. SNOTEL is a network of automatic weather stations (AWS) in snow-dominated watersheds across the western United States, operated by the USDA NRCS Snow Survey. The SNOTEL stations provide hourly measurements of snow depth with a precision of 0.013 m . Additionally, at Mores Creek, multiple 1 m resolution airborne lidar surveys of snow depth across the Mores Creek AOI were flown over the 2022–2024 winter seasons. Each site is described in more detail below.

We use the ATL06_SR product for all available ICESat-2 data acquired from October 2018 to April 2024 within the boundaries of the four study sites. We refer the reader to and for detailed description of the ATL06_SR product used herein. Briefly, to calculate ATL06_SR, we applied the ATL06 function to ATL08 ground-classified ATL03 photons . We calculated ATL06_SR using the SlideRule Earth data processing package which allows for rapid, cloud-based processing of the ATL03 photon cloud with customized control of the ATL06 algorithm parameters . For this study ATL06_SR was calculated using ATL08 ground-classified ATL03 photons using otherwise default ATL06 parameters: a 40 m segment length, a step size of 20 m, a minimum along-track spread of 20 m, a maximum of 6 iterations, and a minimum of 10 ATL08 ground classified photons. The resulting ATL06_SR product therefore has an elevation estimate every 20 m. We use the ATL06_SR h_mean parameter – the elevation at the center of a linear fit of the photons within the 40 m segment, equivalent to the area-averaged elevation – as h_IS2 for our analysis. The ATL06_SR h_mean parameter linear fit uses an iterative selection refinement to remove noise from miss-identified photons but does not include the transmit-pulse-shape correction or the first-photon-bias correction included in ATL06's land ice height parameter (h_li) . Since the ATL06_SR h_mean parameter is evaluated at the center of the ATL06_SR segment, we refer to the nominal location of the elevation data as the centroid. The ATL06_SR and reference DTM data are reprojected to WGS84 UTM zone 11N (EPSG:32611). The native coordinate reference frame (CRS) for ICESat-2 is the WGS84 ellipsoid (EPSG: 4326). The native CRS for the snow-free reference DTMs is the North American Datum 1983 in the horizontal (EPSG: 26911) and the North American Vertical Datum 1988 (EPSG: 5103) geoid heights in the vertical.

Geolocation offsets increase uncertainty and introduce error in the interpretation of ICESat-2 elevation data compared to the DTM, especially in sloped terrain. The magnitude of the error depends on the magnitude of the geolocation offset as well as the surface slope and aspect relative to the horizontal direction of offset . Since the snow-free reference DTMs of each site are independent of each other, ICESat-2 and the reference DTM must be co-registered on a site by site basis. Accurate co-registration relies on stable surface matching, thus only snow-free ICESat-2 elevation data are used for co-registration. Snow-free ICESat-2 elevations are identified using the temporally closest Sentinel-2 (courtesy of European Space Agency, Copernicus) or Landsat 8/9 (courtesy of NASA and USGS) derived snow cover map. Snow cover is identified using the NDSI, wherein 3NDSI=ρgreen-ρSWIRρgreen+ρSWIR where ρgreen and ρSWIR are the surface reflectance in the green and SWIR bands respectively. ρgreen and ρSWIR are bands B3 and B11 for Sentinel-2 imagery and bands SR_B3 and SR_B6 for Landsat 8/9 imagery . For each study site, NDSI time series are created using all Sentinel-2 and Landsat 8/9 images covering at least 70 % of the AOI and with < 10 % cloud-cover in the AOI during our observation period (2018–2024). Pixels with an NDSI > 0.4 are classified as snow . ATL06_SR segments are assigned as snow-covered or snow-free based on the classification of the nearest neighbor snow cover pixel.

After identifying the snow-free ICESat-2 elevation data, ATL06_SR and the site DTM are co-registered using an iterative grid search algorithm that is similar to the iterative co-registration algorithm used in to reduce errors in DTMs of the rugged Qinghai-Tibet Plateau. First a coarse (1 m increment) grid search is performed over a grid of ±8 m in the easting and northing directions – almost double the ICESat-2 geolocation uncertainty of ∼ 4.4. m – to find the approximate location of the global minimum of the snow-free ICESat-2 elevation residual NMAD. A finer (0.1 m increment) grid search is then performed within ±0.9 m of the coarse grid search's minimum to identify the true global minimum of the snow-free ICESat-2 elevation residual NMAD. At each coordinate in the transform grid the mean reference elevation in each ICESat-2 segment is calculated to downsample the reference DTM to the geometry of the transformed ICESat-2 tracks before calculating the elevation residual NMAD. In addition to the iterative grid search two other co-registration algorithms were tested and rejected during method development, the co-registration algorithm (as used in ), and a gradient descent (as used in ). These are discussed further in Appendix A.

Most existing ICESat-2 snow depth studies use an aggregate co-registration approach where a single co-registration transform is calculated from all snow-free ICESat-2 elevations and applied to all ICESat-2 tracks . We test both an aggregate co-registration approach using all snow-free ATL06_SR segments and an individual co-registration for each ICESat-2 overpass using all snow-free ATL06_SR segments from the overpass (Fig. ). For comparison with the results of , who estimated a near-zero offset, and , who applied no horizontal transform, we also test a “no co-registration” approach wherein the ICESat-2 elevation residuals and ICESat-2 snow depths are calculated without any horizontal co-registration transform. Final reported ICESat-2 snow depths are calculated using aggregate horizontal co-registration but discussion of other co-registrations is included for comparison.

After horizontal co-registration, we calculate elevation, aspect, and slope metrics from the reference DTM for each ATL06_SR segment. The reference elevation for each ATL06_SR point is the mean elevation of the DTM within the corresponding ATL06_SR segment area (a 11 m by 40 m rectangle, oriented along the ICESat-2 track). The along-track slope and aspect are calculated from a plane fit to the reference DTM surface within the corresponding ATL06_SR segment area. Although the DTM derived terrain metrics are extracted from within the entire ATL06_SR segment area, the DTM terrain metrics are nominally assigned the same segment centroid coordinates as the ATL06_SR elevation to facilitate analysis.

Vertical co-registration is calculated using snow-free conditions and applied to both snow-free and snow-covered data. Since the snow-free ICESat-2 elevation residuals are not normally distributed, we solve for any vertical bias and the progressive negative slope bias that has been previously identified in ICESat-2 data in mountain regions using the median snow-free elevation bias from slopes of 0 to 40° in 5° steps. Slopes > 40° are excluded to remove outliers. As this progressive slope bias is best described by a quadratic function , we fit a quadratic curve to the median snow-free ICESat-2 elevation residuals relative to slope to solve for site-specific vertical elevation corrections. The vertical bias is assumed to persist in snow-covered conditions, thus the quadratic snow-free vertical bias correction is applied to the snow-covered ICESat-2 returns to minimize biases in snow depth. Transects of 40 m ATL06_SR snow depth estimates are compared to near-coincident airborne lidar snow depth surveys of Mores Creek. To evaluate the scale at which ICESat-2 best captures snow-depth patterns we calculate the median ICESat-2 snow depth within a circle of various radius lengths centered on the AWS, herein we refer to the radius of this circle as the smoothing length. Segment scale spatial variability is evaluated using the NMAD to limit the impact of the heavy-tailed residual distribution while the median snow depth temporal variability is evaluated using the root mean square error (RMSE) as the residual distribution is not heavy-tailed.

The Mores Creek helicopter snow depth surveys are co-registered to the snow-free Mores Creek DTM using HW 21 as a control feature as elevation along the plowed road is stable across seasons (Fig. ) . The aggregate and individual co-registration transforms calculated for the snow-free Mores Creek DTM are applied to the Mores Creek ICESat-2 data to co-register the ICESat-2 data to the Mores Creek helicopter snow depth surveys. For three of the six Mores Creek helicopter survey dates there are insufficient data to calculate an individual co-registration transform (Table ) so those dates are excluded from the individual co-registration analysis.

To compare ICESat-2 snow depths to the helicopter lidar snow depth surveys of Mores Creek, snow depth profiles are calculated along the corresponding ICESat-2 overpass at the ATL06_SR resolution, creating synthetic ICESat-2 tracks (Fig. ). Reference helicopter snow depths are calculated as the average snow depth of the helicopter snow depth survey within the ATL06_SR segment and nominally assigned the centroid coordinates for the corresponding segment.

To facilitate comparison with previous analyses of ICESat-2 snow depth mapping, we calculate bias (i.e., median error) and uncertainty (i.e., NMAD of error) without co-registration, using aggregate co-registration transforms, and using individual co-registration transforms. The magnitude of the individual co-registration transforms have a single direction interquartile range of 3.9 m (Fig. ). In contrast, the magnitude of the aggregate co-registration transforms only reach a maximum of 1.1 m in a single direction (Fig. ). The directions of the individual co-registration transforms are generally NE or SW, with no clear pattern for ascending or descending ICESat-2 tracks. The snow-free elevation residual NMAD is < 0.5 m at Reynolds Creek, ∼ 1 m at Banner Summit and Mores Creek, and ∼ 1.2 m at Dry Creek regardless of co-registration approach. Individual co-registration results in inconsistent changes of ∼ 10 cm to ICESat-2 precision across sites (Table 2). To assess the influence of co-registration approach on snow depth estimates, we compare snow depth from ICESat-2 and synthetic ICESat-2 tracks calculated from near-coincident Mores Creek airborne lidar snow surveys. We find that ICESat-2 snow depth has a negative bias of ∼ 0.6 m and uncertainty of ∼ 1 m regardless of co-registration approach (Fig. , Table ). Additionally, the coefficient of determination (R2) between the ICESat-2 and airborne lidar snow depths indicates stronger correlation between the variables without co-registration or using aggregate co-registration of ICESat-2 (R2=0.47) relative to individual co-registration (R2=0.00).

We attribute the unreliability of the individual co-registration to the abundance of snow cover in the study site: for several winter ICESat-2 overpasses the site's AOI is almost completely snow covered, resulting in < 100 segments for individual co-registration and a high likelihood that segments identified as snow-free are partially snow-covered. The aggregate co-registration uses ∼ 7000–100 000 snow-free segments for co-registration depending on site while the individual co-registration uses an average of ∼ 100–2000 snow-free segments per overpass date depending on site for co-registration. Thus the individual co-registration has orders of magnitude fewer data points available for co-registration, likely skewing transforms for some of the individual tracks.

Uncertainty and bias in ICESat-2 elevation residuals, and therefore snow depths, both increase with slope (Table , Fig. ). Bias is effectively minimized through the application of a quadratic slope-dependent adjustment but the bias adjustment has a slope- and site-dependent impact on uncertainty. At all slopes the quadratic slope-dependent adjustment removes vertical bias but the slope-dependent bias adjustment has little impact on uncertainty. The magnitude of uncertainty increases with slope at all sites (Fig. ). We define shallow, moderate, and steep slopes as < 10, 10–20, > 20° respectively, based on the distribution of slopes across our sites (Fig. a). For shallow slopes site-specific uncertainties range from ∼ 0.2–0.6 m, for moderate slopes uncertainties range from ∼ 0.7–1.0 m, and for steep slopes uncertainties range from ∼ 1.3–1.8 m both before and after applying the slope-dependent bias adjustment (Table ).

To assess the optimal spatial smoothing length of ICESat-2 snow depths in rugged terrain, median ICESat-2 snow depth is calculated within various distances of the AWS, ranging from 50 to 5000 m, at each site. All following ICESat-2 snow depths are calculated after slope corrections are applied. The daily in situ AWS snow depths are used as ground truth. Across all sites 20 %–50 % of ICESat-2 snow depth segments are negative, and thus clearly inaccurate. At all sites, removing negative ICESat-2 snow depth segments improves median ICESat-2 snow depth agreement with AWS snow depth across all smoothing lengths; the RMSE for all ICESat-2 snow depths at each site ranges from 0.3 to 1.9 m, shrinking to 0.2 to 0.8 m when negative ICESat-2 snow depth segments are excluded (Fig. ). If negative ICESat-2 snow depths are not excluded, the median ICESat-2 snow depth systematically underestimates AWS snow depth by an average of 0.54 m across all sites and smoothing lengths; with negative ICESat-2 snow depths excluded, median ICESat-2 snow depth systematically underestimates AWS snow depth by an average of 0.22 m (Fig. ). Because of this improvement to ICESat-2 snow depth accuracy and precision, negative ICESat-2 snow depth segments are excluded from the ICESat-2 snow depth results presented below.

With negative ICESat-2 snow depth segments removed, the median ICESat-2 snow depth generally captures temporal accumulation and ablation patterns over the snow season at the Reynolds Creek, Banner Summit, and Mores Creek AWSs (Figs. , , ). We define the best smoothing length as the length which minimizes snow depth uncertainty while maximizing correlation with the AWS snow depth. At Reynolds Creek and Banner Summit, the AWS snow depth is best captured by ICESat-2 at a smoothing length in the range of 300 to 700 m where the snow depth uncertainty reaches its minimum and the coefficient of determination (R2) for a linear regression fit to the ICESat-2 snow depths relative to AWS snow depths reaches its maximum for the full time period at each site (Fig. ). At Reynolds Creek R2 is also near maximum for both the accumulation season (October–March; 0.85) and ablation season (April–September; 0.80) at the 500 m smoothing scale. At Banner Summit, snow depth R2 is ∼ 0.9 for both the accumulation season and the ablation season at the 500 m smoothing scale. Mores Creek the relationship is variable between Icesat-2 snow depths and the AWS snow depths when the smoothing length is below ∼ 1000 m and shows little change with smoothing length above ∼ 1000 m. Unlike the other sites, Dry Creek's ICESat-2 snow depth uncertainty and correlation with AWS observation are highly variable and do not show a clear trend with respect to smoothing length.

Conversely, when capturing the spatial distribution of snow across a watershed larger smoothing scales have lower uncertainty and greater correlation to observed snow depths. Comparing ICESat-2 snow depths to the Mores Creek Airborne surveys ICESat-2 snow depth uncertainty and correlation with observation improve as the smoothing scale increases Comparison of ICESat-2 snow depths against Mores Creek airborne lidar snow depth indicates that ICESat-2 snow depth uncertainty and correlation both improve as smoothing length increases. The ICESat-2 uncertainty drops from 0.61 to 0.42 m while R2 rises from 0.60 to 0.72 as smoothing lengths increase from 50 to 5000 m. The Mores Creek ICESat-2 snow depth NMAD is below 0.5 m for all smoothing lengths > 800 m and filtered to slopes < 20° (Fig. ). While uncertainty decreases at larger scales we also resolve less detail as spatial scale increases, therefore appropriate smoothing length depends on the snow depth uncertainty and spatial resolution needs of a given application.

To assess ICESat-2's ability to capture terrain dependent variations in snow depth, we calculate the snow depth elevation gradient at 100 m elevation increments using ICESat-2 snow depths within 5 km of the AWS for all sites and airborne lidar for Mores Creek. To reduce outliers, the median ICESat-2 snow depth is not calculated for elevation bins with fewer than 30 ICESat-2 observations. In February and March, the months of near-peak snow depth at the AWS, the ICESat-2 snow depth gradient with elevation is 0.11 m per 100 m of elevation gain at Reynolds Creek, 0.12 m at Banner Summit, and 0.18 m at Dry Creek (Fig. ). At Mores Creek, the ICESat-2 and airborne lidar snow depth gradients with elevation are 0.23 and 0.24 m per 100 m of elevation gain, respectively.

Careful co-registration is a critical step to reduce geolocation errors in the ICESat-2 snow depth signal, yet it remains a challenge in complex snow-covered terrain that lacks stable controls. For our final ICESat-2 snow depth analysis we apply an aggregate co-registration transform calculated from all the snow-free ICESat-2 observations to maximize stable (snow-free) observations. The orders of magnitude more data available for co-registration when the tracks are aggregated help minimize the impact of ICESat-2 noise, misidentified snow cover, and suboptimal terrain for cross-correlating distinct features with high accuracy.

There is no inherent reason why the co-registration of ICESat-2 tracks relative to a reference DTM should be constant over time, yet we found little change in uncertainty and accuracy of ICESat-2 snow depth estimates when applying no co-registration transform and a time-invariant co-registration transform while applying time-variant co-registration transform performed slightly worse than either other co-registration approach in most cases (Table , Fig. ). There is large variability in estimated individuals co-registration transforms which can exceed ICESat-2 geolocation uncertainty (4.4 m; , Fig. ). Most concerningly, the application of a time-variant co-registration transform resulted in no correlation between ICESat-2 snow depths and precise independent snow depth estimates (Table ). The high variability in time-variant co-registration of sets may be due to the limited spatial coverage of an individual overpass. If a given overpass happens to fall over a highly sloped or densely vegetated area the co-registration may be in error due to the influence of slope on ICESat-2 accuracy and precision. The poor performance of individual co-registration transforms in the winter is likely also due to sparse snow-free winter terrain. Snow coverage obscures stable terrain and when < 10 % of the region of interest is stable the accuracy of co-registration decreases with the percent of stable terrain . At the sites in this study, the individual ICESat-2 overpasses frequently have very few snow-free segments (< 10 % of segments).The impact of snow cover on snow-free ICESat-2 segment availability can clearly be seen at Mores Creek where only 50 % of the paired ICESat-2 and Mores Creek airborne lidar dates have any snow-free ICESat-2 returns at all with which to perform an individual co-registration. There are indications of the impact of snow-free segments in the individual co-registration transforms at each site: at Reynolds Creek and Dry Creek, the two sites that span the typical rain–snow transition line and thus often contain both snow-free and snow-covered ICESat-2 segments, there is less variability within the individual co-registration transforms than for the mostly snow-covered Banner Summit and Mores Creek (Fig. ). It is possible that, provided a sufficient amount of snow-free observations, an individual co-registration transform calculated for each ICESat-2 overpass may be more accurate than an aggregate co-registration transform. Individual co-registration may be particularly important for tasked study sites, such as these, because the tasked off-nadir pointing angle can vary by up to 10° and uncertainty increases with deviation from an orthogonal incidence angle . However, for an individual co-registration viable for snow observation, a large portion of the reference DTM must be snow-free in the winter.

Co-registration remains an unsolved problem. Regardless of co-registration approach, ICESat-2 snow depth maintained a negative bias of 0.6 m and uncertainty of 1 m. Vertical co-registration is critical to remove biases between ICESat-2 and independent reference DTMs, such as the large vertical bias present at Banner Summit prior to slope correction (Fig. 4). However, there is likely a limit to the improvement possible from horizontal co-registration. Horizontal co-registration should be considered by default because there can be systematic offsets between ICESat-2 and the reference DTM depending on the georeferencing of the reference DTM, but the time and computation effort required to perform the horizontal co-registration should be weighed against potential improvements if the reference DTM has precise georeferencing.

ICESat-2 snow depth mapping can capture temporal and spatial snow distribution patterns but its efficacy is dependent on surface slope. In this study, we use multiple datasets for comparison error assessment: snow-free ICESat-2 elevations to snow-free reference DTMs; median ICESat-2 snow depths to AWS snow depths; and ICESat-2 snow depths to airborne lidar-based snow surveys. Each has its strengths and weaknesses. The snow-free ICESat-2 comparison to the reference DTM has the most data and is downsampled to the same spatial coverage and resolution as snow-free ICESat-2, but it is only a proxy for snow covered uncertainty. Snow depth uncertainties are generally less than snow-free uncertainties, likely because ICESat-2 returns a stronger signal from the smoother, brighter, and vegetation-free snow surface. The spatial coverage difference between ICESat-2 (a track of points across an area) versus the AWSs (a point observation) likely contributes to differences in the median ICESat-2 snow depth and AWS snow depth. Although airborne snow depths are only available for six dates at Mores Creek, they are likely a better snow depth validation dataset than the AWS snow depth as the airborne survey is downsampled to the same spatial resolution and coverage as ICESat-2. Our comparison with these data indicate that ICESat-2 systematically underestimates observed snow depth but accurately captures orographic distribution patterns across the 38 km² area, including the drop in snow depth at 2000 m elevation (Table , Figs. , ). Though Mores Creek has a higher snow depth uncertainty than Reynolds Creek or Banner Summit due to its steep terrain, uncertainties in ICESat-2 snow depths compared to the airborne snow depth surveys are ∼ 0.5 m when spatially smoothed and ∼ 0.7 m for individual segments, indicating that ICESat-2 is capable of capturing snow depth variability in shallow-to-moderate slope terrain.

Slope strongly influences uncertainty and bias in snow-free ICESat-2 elevations, and therefore snow depths (Table ). As the majority of our in situ snow depth observations are point observations, we use snow-free ICESat-2 elevation residuals to gain insight on the impact of slope on uncertainty. We find snow-free uncertainties of ∼ 0.2–0.6 m for slopes < 10° while the snow-free uncertainty increases by ∼ 1 m or more when slopes are > 20°. While it is difficult to directly assess snow depth uncertainty with respect to slope, the magnitude of snow depth uncertainty at each study site follows this pattern given the distributions of slope at each site; Reynolds Creek and Banner Summit – the sites with the largest proportion of slopes < 20° – have the lowest ICESat-2 snow depth uncertainty and highest R2 across the sites, highlighting the potential utility of ICESat-2 for snow depth observations in shallow-sloped locations (Fig. ). When compared to the Mores Creek airborne snow depth surveys, ICESat-2 snow depth agreement with the airborne observations is distinctly improved by removing observations over > 20° slope terrain (Fig. ). At Dry Creek, where the majority of slopes are > 20°, ICESat-2 snow depths are unreliable.

Steep slopes and abundant, mixed vegetation influence actual snow depths through their influence on wind redistribution and the surface energy balance and influence apparent snow depths through their impact on lidar returns to the sensor. Low bushy vegetation can influence both real and apparent snow depths. Low, dense bushes can be misclassified as ground in the snow free reference DTM and can create the illusion of negative snow depth . Bushes are found in all our sites and likely bias the median reference elevation when misidentified as ground, resulting in apparent negative snow depths. The Reynolds Creek and Banner Summit AWSs are surrounded by rolling and relatively open terrain, likely contributing to both site's small snow depth uncertainty (∼ 0.2–0.4 m). The higher snow depth uncertainty at Dry Creek and Mores Creek (∼ 0.5–0.8 m) is likely due to the steep and vegetated terrain surrounding the AWS at each site. Removing negative ICESat-2 snow depths before calculating the median ICESat-2 snow depth reduces bias and uncertainty of the ICESat-2 snow depth estimates, but is sensitive to the vertical co-registration. If negative values are not removed, the median ICESat-2 snow depth systematically underestimates AWS snow depths (Fig. ). However the data suggests that shallow (< 0.5 m) snow depths may be slightly over-estimated by the median ICESat-2 snow depth when negative ICESat-2 snow depths are removed (Fig. ). The reductions in bias and uncertainty that result from the removal of negative snow depths are greater than if the data are filtered to remove snow depths over slopes > 20°, indicating that at least a portion of the erroneous snow depths are caused by vegetation effects. The overestimation of shallow snow depths could be mitigated by lowering the minimum snow depth threshold below 0 m based on ICESat-2 snow depth uncertainty, however this also increases the impact of outliers on deeper snow depth estimates.

Spatial smoothing of ICESat-2 snow depths can reduce uncertainty, though the optimal smoothing length depends on terrain and application because actual snow depths and errors vary with slope and vegetation. A larger smoothing length will reduce random errors but may span a wide range of snow depths. A smaller smoothing length may span a smaller range of snow depths, making the estimate more directly comparable to a point in situ observation, but will decrease the number of ICESat-2 segment observations within the smoothing length thus increasing the impact of random errors. We find that when trying to capture the temporal snow depth patterns at a AWS (a point observation) snow depth is best captured by ICESat-2 at a smoothing scale in the range of 300 to 700 m. A 500 m smoothing length contains less terrain variability than longer lengths while still containing a reasonable number of ICESat-2 segment observations (average 13 ICESat-2 segments) as opposed to a 100 m smoothing length (average 3 ICESat-2 segments). Conversely by comparing ICESat-2 to the Mores Creek airborne snow depth surveys we find that ICESat-2 snow depth uncertainties and correlation with observed spatial snow distribution patterns increases with smoothing scale, with uncertainties dropping below 0.5 m when smoothing length is > 800 m. To calculate the snow depth elevation gradient we were able to maintain larger numbers (> 30) of segment observations at a 100 m scale by grouping the data into elevation zones across the watershed rather than 100 m spatial regions. Grouping the ICESat-2 snow depth data into elevation zones may be more effective for characterizing snow depths across a landscape than directly calculating spatial distribution as it maintains a high spatial resolution while averaging over many data points to reduce variability. An elevation-based averaging approach inherently assumes that the primary control on snow depth is elevation; generally this applies (Fig. 9), but slope and vegetation density varies greatly across the terrain, resulting in large variation in snow depth at a given elevation. Grouping the data by elevation zones may obscure other terrain controls on snow depth, however some terrain controls on snow depth may also be obscured by estimating snow depth at the larger spatial smoothing scales required to achieve similar data density. The snow depth averaging approach should be selected based on a given project's needs and these sampling considerations.

ICESat-2 snow depth mapping is promising, capturing spatial and temporal distribution patterns at scales of 100–1000 m; however, ICESat-2 snow depths are not reliable in all conditions. Based on the results for our study sites, we recommend using ICESat-2 snow depth mapping in regions with a majority of slopes < 20°. For example, at Mores Creek (Fig. a), when ICESat-2 returns from steep slopes (> 20°) are filtered, snow depth uncertainty is ∼ 0.3–0.7 m. Although ICESat-2 snow depth uncertainties can be as low as 0.2 m where the majority of slopes are < 10°, based on the relative abundance of shallow-sloped regions at our sites and across Idaho more broadly, restricting ICESat-2 application to such shallow-sloped regions will limit their usefulness. Our work reveals that slope introduces a progressive negative bias and increasing uncertainty. Calculating and applying a site specific slope correction removes the progressive bias and reduces uncertainty up to 30 % so ICESat-2 can be used for snow depth observation in more complex terrain with appropriate spatial averaging.

As with all lidar techniques, care must be taken when interpreting snow-covered ATL06_SR elevations with respect to a reference DTM in regions where low matted vegetation is present , regardless of slope. Deep snow covers and smooths low vegetation and small-scale topographic roughness, combined with the high reflectiveness of the snow surface this increases photon return density and accuracy resulting in a more precise snow signal relative to regions with a shallow snowpack . The effects of vegetation on snow depth uncertainties are demonstrated through a comparison of Mores Creek and Banner Summit: though Mores Creek and Banner Summit have similar slope distribution, the snow depth uncertainties at Mores Creek are slightly larger than for Banner Summit likely due to the abundance of low bushes in close proximity to the Mores Creek AWS. However, the snow depth uncertainty for Mores Creek is ∼ 1 m less than for Dry Creek despite similar vegetation at both sites, which we attribute to the combined effects of more snow-compressed vegetation and shallower slopes at Mores Creek on lidar returns. Even with these corrections, sites like Dry Creek, where steep slopes (majority > 20°) and bushy terrain increase snow depth uncertainty to 1.5 m and snow depth error to 1.2 m, are ill-suited for ICESat-2 observation.

As a reference, we demonstrate where ICESat-2 is expected to yield useful snow depth estimates in Idaho based on slope and the snow depth relative to an estimated uncertainty of ∼ 0.5 m. We use the 30 m NASADEM to estimate slope and the average March SNODAS model output to estimate peak snow depths (Fig. ). The state is first classified by slope at 10° increments, then the slope classes are parsed based on their approximate snow depth (Table ). Although uncertainties in SNODAS and the NASADEM are large, the classified map of Idaho demonstrates why Mores Creek is a reasonable site for ICESat-2 snow depth mapping but Dry Creek is not: though Mores Creek is predominantly steep terrain, the snowpack is deep, whereas Dry Creek is steep and has a shallow snowpack. In contrast, Banner Summit, where we see the lowest ICESat-2 snow uncertainty and highest correlation with in situ snow depth, has a deep snowpack and contains shallow-sloped regions that are ideal for accurate ICESat-2 snow depth estimates. In addition to these slope and snow depth thresholds, we recommend that future applications of ICESat-2 consider both the density and type of vegetation in the study region to maximize the likelihood of canopy penetration and ground identification.

Here we use the NASADEM for visualization of slope ranges, however we do not recommend NASADEM for ICESat-2 snow depth mapping due to its coarse resolution (30 m) and potential vegetation effects. Fortunately, there are publicly available high resolution (< 5 m) DTMs of many snow dependent regions. For example, the USGS 3D Elevation Program (3DEP) has publicly available 1 m resolution DTM coverage for over 70 % of the Western United States and is working toward 100 % coverage. Other mountain regions also have high resolution lidar DTM coverage, such as the Swiss national DTM (swissALTI3D). Utilizing these snow-free DTMs in conjunction with ICESat-2 data has the potential to drastically expand snow observation in mid-latitudes.